# Settlement types, definitions, and general equation

Courses > Foundation Analysis and Design > Settlement of Shallow Foundations > Settlement types, definitions, and general equation

### Introduction

Excessive foundation settlements can impair the serviceability and even the safety of a structure. Settlements are due to either volume change or distortion of the soil and can take place immediately or over a time that could be measured in years. Immediate settlements are estimated using equations from elasticity theory, while long-term settlements are calculated using the concepts of consolidation. An essential design step consists of the comparison of these estimates with the stipulated tolerable settlements: A well-designed foundation will settle less than what is deemed tolerable.

### Concepts and Formulas

#### Deformation in soils

1. All soils deform when stress is changed (given time). Deformation may be immediate and/or may take a long time to occur.

2. Types of deformation:

• Distortion of the soil mass (change in shape without a change in volume)
• Changes in volume of the soil mass:
• Changes in shape or breakage of grains
• Compression of pore air, pore water, or both
• Reorientation and movement of particles relative to other particles

#### Treatment

General equation for total settlement: St= Si+ Sc+ Ss+ Sm

where

St = total settlement
Si = immediate settlement

Immediate settlement results from distortion of soil mass caused by a change in total stress. Si is zero for true one-dimensional compression but is not zero for two or three-dimensional compression

Primary compression results from changes in effective stress and is time-dependent

Secondary compression (volumetric “creep”) occurs with time at constant effective stress

Sm= settlement induced by changes in moisture condition (wetting or drying)

Expansive soils are susceptible to swell and shrinkage. All soils may be collapsible under certain conditions, so the potential for settlement from collapse should always be considered.

1.  Saturated inorganic silts and clays: Sc usually dominates, some Si and some Ss
2.  Granular soils and partially saturated clays: Si dominates, some Ss
3.  Highly organic soils and peats: Si and Ss, some Sc (may be insignificant)

#### Definitions

Compression : distortion and changes in volume occurring as a result of imposed stresses but not those accompanying failure

a. Distortion of soil mass - change in shape of soil mass without a change in volume
b. Change in shape or fracturing of particles - generally not a significant component of total settlement
c. Reorientation and movement of particles

Consolidation : a special case of compression in which the soil is saturated and fine-grained, and the changes in volume are time-dependent and occur when water is expelled from the voids

Settlement : a decrease in elevation experienced on or within a soil as a result of compression

Heave : an increase in elevation experienced on or within a soil as a result of decompression

One-dimensional compression : all volume change occurs only in one direction (usually the direction of applied stress). For the situations we will consider, volume change is assumed to occur only in the vertical direction.

Swell : an increase in volume that occurs when an expansive soil gets wetter

Collapse : a decrease in volume that occurs when a soil gets wetter

Shrinkage : a decrease in volume that occurs when a soil dries out

#### General Equation

Generally, total settlement is equal to the integration of vertical strain over the depth of influence below the bearing level:

$S=\int_{z_{f}=0}^{z_{f}=z_{f0}}\varepsilon _{v}dz$

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